This post confuses me. Why would code be simpler than the math notation? Both involve symbolic abstraction of basically the same complexity

i hate that we all got so frightened about math. it's genuinely fun to learn how it works when you're not being forced to in a school setting, which was just a fucking nightmare for no reason. i had this former navy DI lady teacher in gifted kid algebra [so already a year ahead] yell at me for asking questions; she wasn't going to 'hold my hand' thru the homework, which was quite literally her fucking job

When you study CompSci (depending on where IG) you tend to see them that way when trying to mathematically prove something about an algorithm. It's only really a good way of thinking if you're into coding, but I don't think a teacher for a non-coding related algebra class should show this, it can be really confusing for some people.

People who are arguing that one way of expressing these concepts is easier to learn/understand than the other are missing the whole point. Mathematical notation was not designed to teach students how to do math or explain how to design algorithms. It was invented to communicate precise, abstract ideas concisely between mathematicians who already understand what the symbols mean.

Mathematicians require a notation that has the flexibility to manipulate mathematical objects/symbols in a way that naturally emphasizes their properties and relationships. Often they don't even care whether the objects they're studying are even computable or have a numerical representation. They just need them to have certain properties so that they can be manipulated appropriately.

Discrete sums are a rare example of when the mathematical notation overlaps with the description of an algorithm for computing its value (and the overlap is not even complete; infinite sums are easily represented in math notation but are practically uncomputable when implemented naively). Every other advanced mathematical concept puts a premium on ease of symbol manipulation over computability: integrals, derivatives, matrix multiplication, abstract algebra, etc.

TL;DR math notation is complex because its intended audience is people who already understand it, want maximum flexibility of symbol manipulation, and historically didn't really care about practical computation.

These scary large math symbols aren't scary at all and easily explained. The scary parts of maths lie elsewhere. They are discrete, nonlinear or high dimensional and sometimes even the numbers are complex... Or worse.

Yea that's not explained better than a math teach. They just swapped notation common in math, for notation common in one specific programming language. it's only easier for the audience who happens to be familiar with programming in general, and that language in particular.

Which makes the integral sign ∫ a non-discrete for-loop

Maybe I'm crazy but they did teach me this in school. "This means so this operation until conditions are met".

I have no idea what these math things are but I understand the code perfectly lol

Wow, this is by far the clearest I've ever seen this explained.

Just notational difference other than presence of mutation.. How is it harder to understand 3 + 6 + 9 + ... + 3n means compared to the for loop? Is repeated addition hard to grasp?

Fuck! Im 40 and this is the first time I understand the sigma sign!! Thank you!

Couldnt they just show this to me at 7th grade or something when i already learned pascal?

While I acknowledhe that I had some pretty awful math teachers, I would like to add that explaining math concepts in an edited video that you could spend a lot of time making has different demands than babysitting/teaching 30+ students at different levels multiple times a day with little prep time.

The hard part of math isn't understanding esoteric symbols it's the theory behind it and it's application. Number theory will mindbreak almost all people.

Ok but this is a bit of an unfair comparison given that Freya is pretty god tier at actually explaining math things.

You can reduce this readable code into one line of confusing python list comprehension that runs 100x slower!

than

Better then

In a way I always thought coding was more intuitive than maths writing norms. That is if you speak English. If not, it's as much daunting as weird greek symbols.

I remember how confused I was when I first encountered i=i+1... like, what 🤨? How can this be correct, this thing has to be wrong... and then you start seing the logic behind it and you're like "oooh, yeah, that seems to work... but still, this is wrong on almost every level in math"... and then you grow a bit older and realize that coding has nothing to do with math, instead it's got everything to do with problem solving. If you like to name your variables peach, grape, c*nt, you can, and if that helps you solve the problem, even better, just make it work, i.e. solve the problem 🤷.

Sorta not really related but Freya's video on splines ("The Continuity of Splines") is a virtually perfect resource if you're interested in learning about... well... splines.